How can put a mesh into a different position?
Align identical object by a twin tris
Let's suppose you have an object and another one, very similar to the first, and you want to overlay the two.
If they are not perfectlty identical, you should probably start an iterating computation that would progressively guess the function that best fit all the vertex positions...
...if instead they are identical (as in your case), but with different transformations applied such as in the picture below:

the problem is much more simple. If you'll get able to align one triangular face to the corrispective one, the whole mesh will be aligned. I would suggest to use the Precise Align add-on.
Basically you have to activate edit mode of both object (one at time), select the same triangular faces by selecting the vertices in the same ordere and than create a parented empty with the add-on command:

These two empty are now associated with the mesh. All you have to do is to match position and rotation of the empty object and the two jaws will follow their trasformation:

Overlapped!


Limit object's rotation
Easiest way to set up a moving jaw is to first of all add an empty that would represent the rotation pivot and than parent the upper jaw to it.

Now the jaw will follow empty's transfrormations.

Add a Limit Rotation constrain to the empty and assign min e max angles to limit the rotation of the jaw to a given range too.
Credits: jaw's model by lucasfalcao from Blendswap